Related papers: The potential of discs from a "mean Green function…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
We infer the gravitational potential of the Galactic disk by analysing the phase-space densities of 120 stellar samples in 40 spatially separate sub-regions of the solar neighbourhood, using Gaia's second data release (DR2), in order to…
Under a largeness assumption on the size of the residue field, we give an explicit description of the positive-depth Deligne--Lusztig induction of unramified elliptic pairs $(T,\theta)$. When $\theta$ is regular, we show that positive-depth…
We obtain two equations (following from two different approaches) for the density profile in a self-gravitating polytropic cylindrically symmetric and rotating turbulent gas disk. The adopted physical picture is appropriate to describe the…
It is shown how the well-known formula for the gravitational energy of self-gravitating regular polytropes of finite mass can be obtained in an elementary way by using Gauss's divergence theorem and the Chandrasekhar virial tensor, without…
In a disc galaxy the distribution of azimuthal components of velocity is very skew. In the past this skewness has been modelled by superposed Gaussians. We use dynamical arguments to derive an analytic formula that can be fitted to observed…
We determine the surface density of matter in the disc of the Galaxy at the solar position using K giant stars. The local space density and luminosity function of the giants is determined using parallaxes from the Hipparcos satellite; for…
Although the Eddington limit has originally been derived for stars, recently its relevance for the evolution of accretion discs has been realized. We discuss the question whether the classical Eddington limit - which has been applied…
In a recent series of papers, the authors introduced a new Relativistic Newtonian Dynamics (RND) and tested its validity by the accurate prediction of the gravitational time dilation, the anomalous precession of Mercury, the periastron…
An approach for examination of gravitational theories using precision measurements of particle lifetime is proposed. The expressions describing dependence of particle lifetime on gravitational potential in Einstein's and Newton's gravity…
We study particle dynamics in local two-dimensional simulations of self-gravitating accretion discs with a simple cooling law. It is well known that the structure which arises in the gaseous component of the disc due to a gravitational…
We examine the effect of self-gravity in a rotating thick-disk equilibrium in the presence of a dipolar magnetic field. In the first part, we find a self-similar solution for non-self-gravitating disks. The solution that we have found shows…
We present analytic models for the local structure of self-regulated self-gravit ating accretion discs that are subject to realistic cooling. Such an approach can be used to predict the secular evolution of self-gravitating discs (which can…
Coarse-grained spin density functional theory (SDFT) is a version of SDFT which works with number/spin densities specified to a limited resolution --- averages over cells of a regular spatial partition --- and external potentials constant…
Closed expressions for the Green function and amplitude of the scalar particle scattering in the external gravitational field $g_{\mu\nu}(x)$ are found in the form of functional integrals. It is shown that, as compared with the scattering…
This is a sequel to arXiv:2401.02087. We prove the Green function rigidity conjecture in arXiv:2401.02087 for conformal Laplacian in dimension $n\geq 3$. For the Paneitz operator, we prove the Green function rigidity conjecture when $n\neq…
We study theoretically the energy and spatially resolved local density of states (LDoS) in graphene at high perpendicular magnetic field. For this purpose, we extend from the Schr\"odinger to the Dirac case a semicoherent-state…
A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and…
We will find Green's function for the standard weighted Laplacian and use the corresponding Green's potential to solve Poisson's equation in the unit disc with zero boundary values, in the sense of radial $L^1$-means, for complex Borel…
We present accurate models of the gravitational potential produced by a radially exponential disk mass distribution. The models are produced by combining three separate Miyamoto-Nagai disks. Such models have been used previously to model…